1. Technical Field
This disclosure relates to feedback control systems for flexible mechanical systems which suppress modal frequencies in a control signal.
2. Description of Related Art
Flexible dynamics can occur in numerous mechanical systems in which control systems seek to maintain stability or increase tracking performance. Unless accounted for by the control scheme, these dynamics can cause instabilities or degradation in performance.
A notch filter has been used to suppress the flexible modes. However, the modal frequencies may be unknown and may even vary over time. This has been dealt with by using a notch wide enough to encompass these variations. Such an approach, however, may degrade performance.
One such system is a pointing system using flexible actuators. As the notch filter becomes wider, however, it may induce greater magnitude and phase lag at lower frequencies, resulting in a lower bandwidth system.
Another approach has been to use an adaptive notch filter. This is a notch filter whose center frequency varies to track the modal frequencies of the system. The adaptive notch filter has been studied in signal processing research, see J. M. T Romano and M. Bellanger, “Fast least square adaptive notch filtering,” IEEE Trans. Acoust., Speech, Signal Process., vol. 36, no. 9, pp. 1536-1540, September 1988; P. A. Regalia, “An improved lattice-based adaptive IIR notch filter,” IEEE Trans. Acoust., Speech, Signal Process., vol. 39, no. 9, pp. 2124-2128, September 1991; and M. V. Dragosevic and S. S. Stankovic, “An adaptive notch filter with improved tracking properties,” IEEE Trans. Signal Process., vol. 43, no. 9, pp. 2068-2078, September 1995 as well as in applications such as a hard disk drive, see K. Ohno and T. Hara, “Adaptive resonant mode compensation for hard disk drives,” IEEE Trans. Ind. Eng., vol. 53, no. 2, pp. 624-630, April 2006, launch vehicles, see M. J. Englehart and J. M. Krauss, “An adaptive control concept for flexible launch vehicles,” presented at the AIAA Guid., Nav. Control Conf., Hilton Head, S.C., August 1992, aircraft, see R. K. Mehra and R. K. Prasanth, “Time-domain system identification methods for aeromechanical and aircraft structural modeling,” J. Aircraft, vol. 41, no. 4, pp. 721-729, July 2004, and space structures, see T. W. Lim, A. Bosse, and S. Fisher, “Adaptive filters for real-time system identification and control,” J. Guid., Control, Dyn., vol. 20, no. 1, pp. 61-66, January 1997.
An adaptive notch filter was used on a model of a booster from the Advanced Launch System (ALS) program. The least squares estimator used a simple un-damped resonator as the model for estimation. However, the resonant mode was very pronounced. In other applications, full plant parameterizations was necessary when the flexible mode was not as significant. A probe signal may also be required which may degrade performance
Another strategy for the estimation of the notch filter center frequency uses frequency weighting functions. See K. Ohno and T. Hara, “Adaptive resonant mode compensation for hard disk drives,” IEEE Trans. Ind. Eng., vol. 53, no. 2, pp. 624-630, April 2006, The downside may be that there are several failure modes that are known and avoidance requires some modal information a priori.
A stochastic state space algorithm for mode frequency estimation has also been proposed. See R. K. Mehra and R. K. Prasanth, “Time-domain system identification methods for aeromechanical and aircraft structural modeling,” J. Aircraft, vol. 41, no. 4, pp. 721-729, July 2004, However, it relied on the injection of a probe signal. An indirect adaptive compensation (IAC) scheme also required a probe signal to complete the estimation. An adaptive mode suppression scheme may use a Least mean squares (LMS) algorithm to update filter coefficients and the modal parameters may then be extracted from the filter. See T. W. Lim, A. Bosse, and S. Fisher, “Adaptive filters for real-time system identification and control,” J. Guid., Control, Dyn., vol. 20, no. 1, pp. 61-66, January 1997, These approaches may either require the injection of an additional signal for parameter identification or may not update the adaptive notch filter in real-time. These drawbacks may not allow them to function efficiently on a variety of system.